# Thermodynamics: Calculating mass of air over a change in pressure/temperature

• MrNathan
In summary: There is not a specific directory of thermodynamic equations on this website, but most of the equations can be found in textbooks or online.
MrNathan

## Homework Statement

A vessel of capacity 3 m3 contains air at a pressure of 1.5 bar and a
temperature of 25o C. Additional air is now pumped into the system until the
pressure rises to 30 bar and temperature rises to 60o C. The molar mass of air
is 28.968 g/mol.

## Homework Equations

Calculate:
(i) The mass of air pumped into the system.

## The Attempt at a Solution

I am not sure of the equation i should be using. I thought i should be using n=m/M but i do not know number of moles.

PS: This is my own revision and not homework. I have a University exam on monday and am struggling loads with thermodynamics. I feel I am missing a lot of the equations i should need, does anyone have a link to a list of them? The material my lecturers gave me is not very helpful.

Thanks
Any help appreciated

Nathan

Try PV = nRT

AM

what is n though? is this not a constant? i am not given it in the question

Oh i see, use pv = nRT to work out n.

ok, so from n = PV/RT, am i right in assuming the values of p, V and T are the differences?

n = pV/RT so n = (2850000 x 3)/(8.314 x 35)
n = 29382.45

m = nM so m = 851150.9

Im sure this is wrong as it seems too large.

MrNathan said:
Oh i see, use pv = nRT to work out n.

ok, so from n = PV/RT, am i right in assuming the values of p, V and T are the differences?

n = pV/RT so n = (2850000 x 3)/(8.314 x 35)
n = 29382.45

You have to be careful of the units. 1.5 bar is 150 kPa = 150000 N/m^2

Temperature has to be in Kelvin: 25 C = 298 K

So:

$$n = \frac{PV}{RT} = \frac{150000 \times 3}{8.314 \times 298} = 181.6 \text{moles}$$

AM

Last edited:
ah ok. thanks for the help. like i said above, do you have a directory on this site, or know a link to one, of all the thermodynamics equations?

## 1. How is the mass of air affected by changes in pressure and temperature?

The mass of air is directly proportional to both pressure and temperature. As pressure increases, the air molecules become more closely packed, resulting in an increase in mass. Similarly, as temperature increases, the air molecules gain more energy and move faster, also resulting in an increase in mass. Therefore, changes in pressure and temperature will have a direct impact on the mass of air.

## 2. What is the equation for calculating the mass of air in thermodynamics?

The equation for calculating the mass of air is given by: mass = (pressure * volume) / (gas constant * temperature). This equation is known as the ideal gas law and is commonly used in thermodynamics to determine the mass of a gas.

## 3. How does the ideal gas law affect the calculation of mass of air?

The ideal gas law takes into account the relationship between pressure, volume, temperature, and the number of moles of a gas. It helps to determine the mass of air by considering the pressure and temperature at a specific volume. This equation is useful for calculating the mass of air in various thermodynamic processes.

## 4. Can changes in humidity affect the mass of air?

Yes, changes in humidity can affect the mass of air. Humidity is the amount of water vapor present in the air, and it can impact the density of the air. As humidity increases, the air becomes less dense, resulting in a decrease in mass. Conversely, as humidity decreases, the air becomes more dense, resulting in an increase in mass.

## 5. What are some practical applications of calculating the mass of air in thermodynamics?

Calculating the mass of air is essential in many practical applications, such as weather forecasting, air conditioning and heating systems, and combustion engines. It is also crucial in studying the behavior of gases and the effects of changes in pressure and temperature on air masses.

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